Long and short scales

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Template:TOCright Long scale is the English translation of the French term échelle longue, which designates a system of numeric names in which the word billion means a million millions.

Short scale is the English translation of the French term échelle courte, which designates a system of numeric names in which the word billion means a thousand millions.

For most of the nineteenth and twentieth centuries, the United Kingdom uniformly used the long scale, while the United States of America used the short scale, so the two systems were often (and accurately at that time) referred to as "British" and "American" usage, respectively. However, today the United Kingdom uses the short scale so widely that the term "British usage" is no longer an appropriate phrase.

Both systems have been used in France at various times in history, but France has now settled with the long scale, in common with most other European languages.

Usage note: some Wikipedia articles use the terms long and short scaleTemplate:Ref – although not presently standard terms in English – because they are unambiguous and easily understood.


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Comparison

Value Short Scale Long Scale
103 = 1 000 thousand thousand
106 = 1 000 000 million million
109 = 1 000 000 000 billion milliard (or thousand million)
1012 = 1 000 000 000 000 trillion billion (<math>10^{2*6}</math>)
1015 = 1 000 000 000 000 000 quadrillion billiard (or thousand billion)
1018 = 1 000 000 000 000 000 000 quintillion trillion (<math>10^{3*6}</math>)

For a more extensive table, see names of large numbers.

Since bi refers to 2 and tri refers to 3, the logic in the names is:

long scale billion: Billion is <math>(10^{6})^{2}</math> = <math>10^{12}</math>. Trillion is <math>(10^{6})^{3}</math> = <math>10^{18}</math>.
short scale billion: Billion is <math>10^{((2+1)*3))}</math> = <math>10^{9}</math>. Trillion is <math>10^{((3+1)*3))}</math> = <math>10^{12}</math>.
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History

1475 Jehan Adam recorded the words "bymillion" and "trimillion" as meaning 1012 and 1018 respectively.
1484 French mathematician Nicolas Chuquet, in his article "Triparty en la science de nombres"[1], used the words byllion, tryllion, quadrillion, quyllion, sixlion, septyllion, ottyllion, and nonyllion to refer to 1012, 1018, etc. Chuquet's work was not published until the 1870s, but most of it was copied without attribution by Estienne de la Roche and published in his 1520 book, Larismetique.
ca. 1550 Jacques Peletier retained Chuquet's long scale but suggested the name milliard in place of "thousand million". This word was widely adopted in England, Germany, and the rest of Europe.
Early 1600s In France and Italy, some scientists began using "billion" to mean 109
Mid 1700s The short-scale meaning of the term "billion" was brought to the British American colonies.
Early 1800s France partially converted to the short scale, and was followed by the USA, which began teaching it in schools.
1926 H. W. Fowler's Modern English Usage noted "It should be remembered that ["billion"] does not mean in American use (which follows the French) what it means in British. For to us it means the second power of a million, i.e. a million millions (1,000,000,000,000); for Americans it means a thousand multiplied by itself twice, or a thousand millions (1,000,000,000), what we call a milliard. Since billion in our sense is useless except to astronomers, it is a pity that we do not conform."
1948 The Conférence Générale des Poids et des Mesures, meeting in France, proposed a return to the long scale.
1961 The Journal Officiel (the official French gazette) confirmed the official French use of the long scale (Décret 61-501, page 4587, note 3, as modified by the erratum on page 7572).
1974 British prime minister Harold Wilson explained before the House of Commons that UK government statistics would from now on use the short scale. [2] Template:Fact
1994 The Italian government officially confirmed the long scale. (Direttiva CE 1994 n. 55, page 12).
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Current usage

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Countries using neither short nor long scales

The following countries have their own numbering systems and use neither short nor long scales:

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Short scale countries

  • Most English-speaking countries — the U.S., Canada (except French-speaking parts), United Kingdom, Ireland, Australia, etc. Template:Fact
  • Brazil, which despite speaking a variant of Portuguese, uses 109 = bilhão, 1012 = trilhão, etc.
  • India, where the Indian numbering system is commonly used, the short scale is also understood by English speakers, since there is no overlap in terms.
  • Russia and Turkey, where 109 is commonly called "milliard" (milyar in Turkish) but the short scale is used for 1012 and above .
  • Greece, which uses 109 = disekatommyrio ("bi-hundred-myriad"), 1012 = trisekatommyrio, ("tri-hundred-myriad"), etc
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Long scale countries

  • Most other countries. Examples:
French, Danish and Norwegian milliard, German Milliarde, Dutch miljard, Hungarian milliárd, Hebrew milliard, Spanish millardo, but more frequently one says "mil miliones", Italian miliardo, Polish miliard, Swedish miljard (or less common milliard), Finnish miljardi, Latvian miljards, Czech miliarda, Romanian miliard and Slovenian, Croatian, Serbian milijarda and Icelandic milljarður all equal 109.
French, Norwegian and Danish billion, German Billion, Dutch biljoen, Spanish billón, Polish and Serbian bilion, Swedish biljon (or less common billion), Finnish biljoona, Croatian bilijun, Portuguese (Portugal) bilião, Slovenian bilijon, Icelandic billjón - all equal 1012.
  • Also, Puerto Rico, a Spanish-speaking US territory but generally uses 1012 = billón, 1018 = trillón, etc.
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Notes

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Italian usage

In Italian, the word bilione officially means 1012. Colloquially, bilione can mean both 109 and 1012; trilione both 1012 and (rarer) 1018 and so on. Therefore, in order to avoid ambiguity, hardly anybody uses them. Forms such as mille miliardi (a thousand milliards) for 1012, un milione di miliardi for 1015, un miliardo di miliardi for 1018, mille miliardi di miliardi for 1021 are much more common.

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UK usage

The term "milliard" is now obsolete in British English (though its derivation "yard" is still used as slang in the London money, foreign exchange and bond markets) and "billion" has meant nothing except 109 in all published writing for many years now. Both the UK government and the BBC use the short scale exclusively in all contexts. Anyone deliberately using billion to mean 1012 in British English is likely to be misunderstood.

However, the long scale understanding still persists, and not only among older people. As numbers this large are rare in everyday life, a significant proportion of lay readers will interpret "billion" as 1012 ("a million million"), even if they are young enough to have been taught otherwise at school. Following this pattern incorrectly, some will even extrapolate "trillion" as a (long scale) billion billions (1024) rather than the actual long scale 1018 or the short scale 1012.

For the above reasons, avoiding the words "billion", "trillion" etc. may be advisable when writing for the general public.

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Australian usage

In Australia, some documents use the term thousand million for 109 in cases where two amounts are being compared using a common unit of one 'million'. The current recommendation by the Australian Department of Finance and Administration (formerly known as AusInfo), and the legal definition, is the short scale. Education, media outlets, and literature all use the short scale in line with other English speaking countries. As at 1999, the Australian Government's financial department did not consider short scales to be standard, but used them occasionally [3]Template:Fact

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Mexican usage

In Mexico, even though the Spanish language has the word "millardo" to mean 109, this word is practically never used, even by the government or the news media, so Mexico should be considered as a long scale country which doesn't use any specific word to mean 109. This quantity is expressed as "mil millones" (a thousand million). "Un billón" (one billion) means a million millions (1012).

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Esperanto usage

The official Esperanto words biliono, triliono etc. are ambiguous, and the inherently international nature of Esperanto communication compounds the problem by preventing any national presumption in favour of long or short scale. Ambiguity may be avoided by the use of the unofficial but generally-recognised suffix -iliono appended to a numeral indicating the power of a million, e.g. duiliono (from du meaning "two") = (106)2 = 1012, triiliono = 1018, etc. Miliardo is an unambiguous term for 109.

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Alternative approaches

Unambiguous ways of identifying large numbers include:

  • Combinations of the unambiguous word 'million', for example: 109 = "one thousand million"; 1012 = "one million million". This becomes rather unwieldy for numbers above 1012.
  • Combination of numbers with more than 3 digits with million, as in 15,300 million.
  • Scientific notation, including its engineering notation variant, for example 109, 1012, or in writing using the computer programming notation (1e9, 1e12, etc). This is the most common practice among scientists and mathematicians, and is both unambiguous and convenient.
  • SI prefixes, for example, giga for 109 and tera for 1012. In information technology contexts, these SI prefixes are sometimes used as powers of 210 (= 1024) instead of powers of 103 (= 1000) , but there is an attempt at introducing a binary prefix system to eliminate this ambiguity.
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References

fr:Échelle longue nl:Korte en lange schaalverdeling zh:数量命名中的级差

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